Single Choice

If $$4\sin^{-1}x+\cos^{-1}x=\pi$$, then $$x$$ is equal to:

A$$\displaystyle\frac{1}{2}$$
Correct Answer
B$$2$$
C$$1$$
D$$\displaystyle\frac{1}{3}$$

Solution

$$4\sin^{-1}x+\cos^{-1}x=\pi$$
$$\Rightarrow 3\sin^{-1}x+(\sin^{-1}x+\cos^{-1}x)=\pi$$

$$\Rightarrow 3\sin^{-1}x+\dfrac{\pi}{2}=\pi$$

$$\Rightarrow \sin^{-1}x=\dfrac{\pi}{6}$$

$$\Rightarrow x=\sin\dfrac{\pi}{6}=\dfrac{1}{2}$$

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